Title: Regularity vs. Condensation in Consensus Dynamics
Abstract:ÌýÌýConsensus is a fundamental mechanism in interacting particle systems and has inspired a wide range of methods in global optimization and pattern formation. We present new results on the propagation of regularity in the presence of superlinear drift terms, which promote condensation effects within consensus dynamics, leading to concentration phenomena even in high-dimensional settings. We then discuss how this perspective extends beyond the original setting to applications in optimization and image segmentation, where data points are interpreted as interacting particles. In this framework, consensus dynamics naturally efficiently drive the emergence of clusters and the detection of coherent structures.